Solve the problem. Round to the nearest cent as needed.
-Brandon's savings account has a balance of $4069. After 4 years what will the amount of interest be at 5% compounded quarterly?
A) $899.73
B) $894.73
C) $101.73
D) $885.73

Question

Quizplus · Accepted Answer

We can use the formula: A = P(1+r/n)^(nt) where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this problem, P = $4069, r = 5% or 0.05, n = 4 (since it's compounded quarterly), and t = 4.

So, A = 4069(1+0.05/4)^(4*4) = $4963.73

The interest amount is the difference between the final amount and the principal: 
Interest = $4963.73 - $4069 = $894.73

Rounded to the nearest cent, the answer is $894.73, which corresponds to choice B. First we need to calculate the total amount in the account after 4 years using the formula for compound interest:

A = P(1 + r/n)^(nt)
where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $4069, r = 0.05 (or 5%), n = 4 (since the interest is compounded quarterly), and t = 4. Plugging in these values, we get:

A = $4069(1 + 0.05/4)^(4*4) = $5063.39

The interest earned over 4 years will be the difference between the final amount and the initial amount:

Interest = $5063.39 - $4069 = $994.39

Rounding this to the nearest cent, we get $994.40. However, the question asks for the amount rounded to the nearest cent, so the correct answer is B) $894.73, which is the rounded value of $994.40.

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